The increase in the processing speed, functionality, and integration in integrated circuits (ICs) has been achieved through continuous reduction in the feature sizes of the ICs. A portion of the manufacturing of the ICs affecting attainable feature sizes is photolithography. During photolithography, a pattern of the IC is transferred from a mask to a wafer, e.g., a semiconducting wafer. Imaging characteristics of modern projection optical photolithography equipment are dominated by diffraction effects. The resolution (i.e. the smallest feature size that can be printed on the wafer) is k1 λ/NA, where λ is the wavelength of the light source, k1 is a constant approximately equal to 0.5, and NA is the numerical aperture of the projection optics. The depth of focus of the projection printer over which the image quality is not degraded is limited and is equal to k2 λ/(NA)2, where k2 is a constant that depends on k1. Thus, to decrease the feature size either the wavelength of exposure must be reduced or the NA of the optics must be increased.
Increasing the optics NA to reduce feature size results in a substantial reduction in the depth of focus (˜(NA)−2), which is undesirable, particularly because the depth of focus must be larger than any variations in the flatness of the photoresist surface. Therefore, the semiconductor industry is pursuing the use of short wavelength exposure sources for achieving smaller and smaller feature sizes. KrF, ArF, and F2 excimer lasers are presently available as light sources for, respectively, 248, 193, and 157 nm photolithography. The synthetic fused silica, however, that has been the optical material of choice for higher wavelength exposure sources, exhibits significant loss of transmittance at wavelengths below 200 nm.
Single crystals of Calcium Fluoride (CaF2) exhibit the desirable optical properties for sub 200-nm-photolithography. Furthermore, for historical reasons the production knowledgebase for CaF2 is relatively extensive. Other single crystals of fluoride such as BaF2 and LiF are also possible material candidates, but are significantly behind CaF2 in production technology, and may be less desirable, e.g., due to toxicity and corrosiveness (BaF2) and/or expense (LiF). Therefore, single crystal CaF2 are desirable and suitable optical material for 193 and 157 nm optical steppers. Presently, CaF2 crystals as large as 30 cm in diameter and 10 cm in height are used in photolithography equipment.
Single crystals of CaF2 are grown by directional solidification from the melt phase. In this process layers of the melt are continuously solidified, by changing the temperature of the crystal, to form a single crystal boule. The crystal boule is subsequently cooled to room temperature. The transfer of heat from and through the crystal sets up temperature gradients (i.e. temperature non-uniformities) and associated thermal stresses in the single crystal. CaF2 is a relatively weak material, especially at elevated temperatures, and therefore experiences plastic deformation under thermal stresses during the crystal growth process. The accumulation of plastic strain during the crystal growth process results in generation of residual stresses in the crystal at room temperature. Residual stresses, in turn, cause stress birefringence through spatial variations in the material's index of refraction, and an associated degradation of optical characteristics of components made from this material.
Annealing is used to reduce residual stresses in crystals that have experienced plastic deformation during the crystals' growth process. To anneal a crystal, the crystal is maintained at an elevated temperature close to its melting point temperature for a period of time. This constant temperature is intended to allow existing residual stresses to relax. The crystal is cooled to room temperature. During cooling, temperature gradients associated with the cooling of the crystal generate thermal stresses in the crystal that may cause the crystal to undergo plastic deformation.
Due to the nature of the material, temperature variations to which a single crystal is exposed to during growth and annealing result in large thermal stresses leading to plastic deformation of the crystal and, hence, large residual birefringence.